The invention relates to a method and a device for sensorless estimation during operation of the relative position between the stator and the rotor of a three-phase synchronous motor comprising a stator having a stator winding comprising terminals for connecting terminal voltage and terminal current, and a magnetic rotor.
In order to achieve an optimum control of the torque developed by a synchronous motor, it is necessary to know the angle between the magnetic flux vector developed by the stator winding during operation and the current vector of the electric current in the stator winding.
In practice, sensors mounted on the shaft of a rotary synchronous motor or, in the case of a linear synchronous motor, a large number of Hall sensors mounted along the track, i.e. the stator of the linear synchronous motor, are inter alia used for determining the aforesaid angle.
The use of sensors of this kind is by no means preferred. The reason for this is that such sensors are generally vulnerably, sensitive to vibration, fouling, incapable of withstanding high temperatures, static electricity, etcetera, but also because separate wiring is required for connecting the sensors. Said wiring is a further source of trouble and generally it also adds significantly to the cost of the installation as a whole.
Determination of the angle between the magnetic flux vector and the stator current vector without making use of mechanical sensors, also called sensorless control, is very important to the industry.
Prior art sensorless methods frequently employ the position-dependent characteristics of a synchronous motor, such as a (small) difference in the inductivity of the stator winding along the so-called (direct) d-axis and the quadrature (q-axis) of the rotor. It is not possible to use this method with linear motors, however, because the air gap between the stator and the rotor (that is, the trolley or the like moving along the track) is relatively much larger with these motors. In addition, with linear motors only part of the stator (the track) is covered by the rotor. An additional problem as regards the determining of the inductivity of the stator winding occurs with linear motors when switched stators are used, that is, wherein just part of the total stator (the track) is constantly activated in dependence on the position of the rotor (the trolley). With linear synchronous motors for high powers and high speeds the system parameters, such as the instantaneous inductivity and resistance of the stator winding, can furthermore change by a large percentage many times per second.
Accordingly, it is a first object of the invention to provide a method for the sensorless provision of an estimate of the relative angular position between the stator and the rotor of a synchronous electric motor, which method can be used both for rotary motors and for linear motors.
In accordance with the invention, this objective is accomplished by means of a method comprising the steps of:
low-pass filtering of the terminal voltage;
low-pass filtering of the terminal current;
high-pass filtering of the terminal current;
determining the rotor speed; and
determining from these filtered magnitudes the relative angular position, corrected with an angular correction derived from the rotor speed.
The invention is based on the insight that an estimate of the magnetic field flux can be obtained by filtering the terminal voltage and the terminal current as described above, so that there is no need for circuits for differentiating the current and for performing open loop integration of the voltage, which are difficult to realise by electronic means.
The instantaneous impedance of the stator winding must be known in order to be able to determine the relative angular position.
In an embodiment of the invention, wherein the stator winding is supplied with electric energy by a pulse width modulator, the impendance is determined from a modulator-induced switching ripple in the terminal voltage and the terminal current.
For determining the switching ripple it is necessary to remove the ground harmonic from the electric energy delivered to the stator winding by the pulse width modulator. The reason for this is that the ground harmonic component does not provide any information as regards the instantaneous inductivity and resistance of the stator winding. Since the synchronous motor is capable of accelerating very quickly in practice, the filtering out of the ground harmonic component by means of conventional low-pass filters is not an option.
In accordance with a further embodiment of the invention, the ground harmonic component is effectively removed from the energy supplied to the stator winding by means of transformation to a system of coordinates that is synchronous to the rotor. In this system of coordinates the ground harmonic component is transformed into a DC component at any possible rotor speed. Once this DC component has been removed, only the switching ripple on the stator current and the stator terminal voltage remains.
In another embodiment of the method according to the invention, the terminal voltage of the synchronous motor is low-pass filtered and the stator current is high-pass filtered and low-pass filtered prior to said transformation, wherein the ground harmonic is removed from the transformed stator terminal voltage and stator current by high-pass filtering, which results in a transformed stator terminal voltage ripple and a transformed stator current ripple.
As a result of said low-pass filtering of the stator terminal voltage the transformed stator terminal voltage ripple corresponds to the terminal flux of the stator winding, so that in accordance with yet another embodiment of the method according to the invention the instantaneous inductivity of the stator winding can be estimated from the quotient of the stator terminal voltage ripple and the stator current ripple, wherein it is assumed that the relation between the current and the flux in a coil is linear, as long as the coil is magnetically unsaturated, of course.
In accordance with the invention said quotient can be advantageously determined from the continuous or running average of the product of the stator terminal voltage ripple and the stator current ripple divided by the continuous or running average of the square of the stator current ripple, wherein these current averages can be determined from low-pass filtering of the products in question.
It has been found that in the case of relatively high-power motors the impedance of the stator winding is generally dominant in comparison with the resistance of the stator winding at any speed. In yet another embodiment of the method according to the invention it suffices to select a fixed value for the stator winding resistance, among which a resistance that equals zero. Generally the error that is thus introduced in the estimated angular position is just small.
With low motor speeds and high current values the terminal voltage of the stator winding may be up to 100 times larger than the internal voltage of the stator winding, as a result of which it is no longer possible to derive the inductivity and resistance for estimating the relative angular position from the switching ripple with a desired degree of accuracy.
For the purpose of determining the relative angular position near standstill of the rotor, the electric energy that is supplied to the stator winding by the pulse width modulator is interrupted in yet another embodiment of the method according to the invention, wherein the stator terminal voltage is measured and the angular position is estimated from the stator terminal voltage measured during the interruption in the energy supply.
This embodiment is based on the insight that the measured stator terminal voltage, when the stator current equals zero, is exactly the same as the internal voltage, which is in turn determined by the change in the magnetic flux. Consequently, it is possible to determine the magnetic flux and thus the relative angular position between the stator and the rotor from the measured terminal voltage.
According to an embodiment of the invention an effective determination of the angular position can be obtained around standstill of the rotor as well by alternately exciting and interrupting the energy supply to the stator winding.
The invention furthermore provides for the automatic switching over from determination of the angular position from the switching ripple on the one hand to determination of the angular position from the interruption of the energy supply on the other hand, in such a manner that when the stator terminal voltage that is measured during the interruption in the energy supply exceeds a predetermined value, the angular position is estimated on the basis of the switching ripple. This method of switching over can be employed for all types of motors with all conceivable stator and rotor configurations on the basis of the highest allowable current value in the stator winding and a desired current value.
In a yet further embodiment of the method according to the invention, compensation is effected for asymmetry effects due to phase switching effects in a three-phase motor and other secondary effects, as well as for low-speed and high-speed rotation of the rotor on the calculated angular position and corrections in the calculated angular positions due to 5th harmonic flux distortion.
The method according to the invention is suitable for determining the relative angular position between the stator and the rotor of synchronous motors comprising a permanent magnetic rotor, an electrically energized rotor, single-phase motors, polyphase motors, rotary motors and linear motors, irrespective of the power thereof.
The invention furthermore relates to a device for estimating the relative angular position between the stator and the rotor of a synchronous motor in accordance with the above-described method, wherein the stator winding is supplied with electric energy by a pulse width modulator.